This study, we introduce a novel Topological Cycle Graph Attention Network (CycGAT), designed to delineate a functional backbone within brain functional graph--key pathways essential for signal transmissio--from non-essential, redundant connections that form cycles around this core structure. We first introduce a cycle incidence matrix that establishes an independent cycle basis within a graph, mapping its relationship with edges. We propose a cycle graph convolution that leverages a cycle adjacency matrix, derived from the cycle incidence matrix, to specifically filter edge signals in a domain of cycles. Additionally, we strengthen the representation power of the cycle graph convolution by adding an attention mechanism, which is further augmented by the introduction of edge positional encodings in cycles, to enhance the topological awareness of CycGAT. We demonstrate CycGAT's localization through simulation and its efficacy on an ABCD study's fMRI data (n=8765), comparing it with baseline models. CycGAT outperforms these models, identifying a functional backbone with significantly fewer cycles, crucial for understanding neural circuits related to general intelligence. Our code will be released once accepted.

本研究介绍了一种新颖的拓扑周期图注意力网络（CycGAT），旨在从非必要、冗余的连接中绘制出脑功能图的功能骨架——信号传输的关键通路，这些连接环绕在核心结构周围形成循环。我们首先引入一个循环关联矩阵，建立了图中的独立循环基础，以映射其与边的关系。我们提出了一种循环图卷积，利用循环关联矩阵导出的循环邻接矩阵，在循环的领域内针对性地过滤边的信号。此外，我们通过在循环中引入边的位置编码，进一步增强了循环图卷积的表示能力，并通过模拟和在一个ABCD研究的fMRI数据（n=8765）上的实验验证了CycGAT的定位能力，将其与基准模型进行了比较。CycGAT优于这些模型，能够识别出功能骨架，并且所需的循环数量明显较少，这对于理解与智力相关的神经回路至关重要。我们的代码将在接受后发布。

脑功能连接的拓扑周期图注意力网络